What is the most efficient way to fill potholes?

The three most common ways to fill potholes are throw and roll, spray patching, and semi-permanent patching. Interestingly, the efficiency of spray patching, semi-permanent patching, and even properly installed cold patch are not that different. The two keys are that the work must be done correctly and that not every pothole or pavement distress can be fix with a patch. How to properly do throw and roll patching is covered in another Quick Answer, "What is the proper technique for filling potholes?".

Finished patch

Our Pavement Management workbook that discusses repair selection and has a chapter on patching.

Another very good resource is the Foundation for Pavement Preservation. I have included a link to their preserving pavement page.

Self-contained spray patch truck

As for spray patching, if you search the internet for spray patching you will find many companies who do this kind of work. A good way to try out the technique is to do a few small areas to start. This is typically done with a rental including the operator. If you like the process you could looking into a longer rental, rental without operator or even a leasing operation.

You can see places where the state has performed spray patching on the interstate (typically a grey area with a slightly course look). The NYS Office of General Services has many contracts that can be utilized for pavement maintenance, but I could not find spray patching as a current contract (it would be under Highway Bituminous Materials).